Economic model predictive control of nonlinear process systems using Lyapunov techniques

• Published in: AIChE journal Vol. 58; no. 3; pp. 855 - 870
• Main Authors: Heidarinejad, Mohsen, Liu, Jinfeng, Christofides, Panagiotis D.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2012; Wiley; American Institute of Chemical Engineers
• Subjects: Applied sciences; asynchronous and delayed measurements; Chemical engineering; Closed loop systems; Cost function; Design engineering; Dynamical systems; economic model predictive control; Economic models; Economics; Exact sciences and technology; Mathematical models; nonlinear process systems; Nonlinear systems; Nonlinearity; Predictive control; Sampling; synchronous measurements; uncertain variables; Closed loop; Stability; nonlinear process systems; Samplings; asynchronous and delayed measurements; uncertain variables; Stability region; Non linear system; Modeling; Steady state; economic model predictive control; Optimization; Design; Upper bound; Economic model; Production; Cost function; Robustness; Sampling; synchronous measurements; Predictive control
• ISSN: 0001-1541; 1547-5905; 1547-5905
• DOI: 10.1002/aic.12672

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012